Let (x): R R be a non-negative function, so that f(x)dx = 1. Show that for...

    

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Let (x): R R be a non-negative function, so that f(x)dx = 1. Show that for any continuous function f : RR, we have that the sequence In(x) = n (n(x-y))f(y)dx converges uniformly on the compact sets of R to f(x). Let (x): R R be a non-negative function, so that f(x)dx = 1. Show that for any continuous function f : RR, we have that the sequence In(x) = n (n(x-y))f(y)dx converges uniformly on the compact sets of R to f(x).